“Let’s Play” Using Manipulatives to Connect the Concrete to the Abstract

1. “Let’s Play”Using Manipulatives to Connect the Concrete to the Abstract Nicole Dorvily Cisely Scott Mathematics Coach Curriculum Support Specialist North County Elementary Education Transformation Office

2. Common Board Configuration (CBC) DATE: August 10, 2011 21, 2011 VOCABULARY: manipulatives,tangram, learning styles, concrete, representational, abstract (CRA), base 10 blocks, geoboards, pattern blocks, virtual manipulatives EXIT SLIP: IN YOUR JOURNAL Connect: How can we use concrete resources to move students to the understanding of representational and abstract math concepts.? Connect: 1 question you still have about the using manipulatives. BENCHMARK: Manipulatives MT 2.0.2011 OBJECTIVE: Participants will explain the purpose of using math manipulatives and identify ways of enhancing math instruction through the use of manipulatives. • AGENDA: • *Icebreaker • *What Are Manipulatives? • *What the Research Shows • *Reaching Various Types of Learners • *Hands-On Activities Rotations • *Demonstrations for Upcoming Benchmarks • *Challenges with prizes • *Virtual Manipulatives • Take Aways: • Things learned during this session • Tangram Handout HOME LEARNING: Review today’s lesson and develop your next steps to use this information in your classroom. ESSENTIAL QUESTION: How can we use concrete resources to move students to the understanding of concepts in the concrete, representational and abstract forms.

3. Ice Breaker (3 minutes) 1. Each of you has a tangram in your group. 2. Your job is to figure out what fraction the smallest triangle represents of the complete tangram.

4. Answer……… What else could we use tangrams to teach?

5. Role Of The Teacher “The mere use of manipulatives does not guarantee that students understand concepts and procedures and be able to connect these concepts to abstract symbols without teachers making these connections explicit.” (Reimer & Moyer 2005)

6. Random Thoughts….. How many of you feel you could become master teachers by just watching a master teacher? How many of you could build a computer after sitting in a computer programming class and listening to your professor tell you how to build a computer? How many of you could fly a plane without ever touching the controls prior to your first flight? Why is this important to the classroom?

7. What Are Manipulatives? • Physical objects used to visualize • abstract concepts and promote learning • Concrete materials that can be • used when exploring math ideas, • performing math tasks or • solving math problems

8. What the Research Says…. • The most valuable learning occurs when students actively construct their own mathematical understanding • Provide opportunities for children to explore, develop, test, discuss, and apply ideas • The use of physical materials is conducive to the concrete kinds of learning that lay the foundation for the development of mathematical understanding NCTM, 2000

9. Some things you might encounter….. Why use manipulatives? They can’t use them on the test? Concrete/Kinestethic Conceptual/Visual Understanding Ability to Understand the Abstract My students can’t behave when they have toys in front of them. • Allow students 1-2 minutes to play with the manipulatives before utilizing them. • Set specific rules i.e. if they hit the floor, you lose yours!

10. C-R-A • CONCRETE: The “doing” stage. Uses hands-on physical (concrete) models or manipulatives to represent numbers and unknowns. • REPRESENTATIONAL : The “seeing” stage. Draws or uses pictorial representations of the models • ABSTRACT: The “symbolic” stage. Involves numbers as abstract symbols of pictorial displays • Conceptual understanding in math will usually follow this order. Therefore it is best to use manipulatives to introduce lesson and/or concept. What grade should we start introducing manipulatives?

11. Why Use Manipulatives? • Motivate students • Feel like they’re playing • Make math learning real and concrete • Prompt discussions about math ideas • Allow teachers to see students at work doing mathematics • Increase engagement • Accommodate various learning styles • Visual learners • Auditory learners • Logical/Mathematical • Musical/Rhythmic • Bodily/Tactile/Kinesthetic learners • Learn through moving, touching, and doing

12. Role Of The Teacher PLANNING IS KEY!!!! • Choose manipulatives to support the lesson’s objectives!! • Provide opportunity to become acquainted with manipulatives before they are used in the lesson • Consider the students when planning the lesson and choosing the appropriate manipulatives • Encourage the students to talk and write about what they have learned. • Help the students to move from manipulatives to paper-and-pencil operations • Discuss observations and to help students draw connections

13. Center 1: Base 10 Blocks Center 2: Geoboards Center 3: Pattern Blocks

14. Stations (5-7 minutes each) Place Value Blocks Activity: Make a list of how these can be used in the classroom and then show me how many ways you can represent the number 123 using base 10 blocks (thousands, hundreds, tens, ones) Geoboard Activity: Make a list of the many things this can be used for, then using a geoboard, show me how you can teach congruent/similar figures and angles Pattern Blocks: Make a list of ways pattern blocks can be used and then show me one equivalent fraction.

15. Geoboards • Aid in the teaching of basic geometric concepts and in developing conceptual understanding of area and perimeter • Improve communication skills, share ideas, and use mathematical vocabulary.

16. Pattern Blocks • A tool to learn and practice fractions • Can be used to familiarize oneself with the different shapes, their relations, and their proportions

17. Base 10 Blocks • Aid to teach Base 10 place value • Basic arithmetic operations • Usually the foundation for understanding of number sense

18. Challenge (with prizes)

19. Choices of Manipulatives • Tangrams • Pattern Blocks • Counters • Geoboard • Base 10 Blocks • Color Tiles (square inch tiles)

20. Challenge 3rd Grade: MA.3.G.3.2 Compose and Decompose Polygons What manipulative and how?

21. Challenge 4th Grade: MA.4.G.3.3 Area of Composite Shapes What manipulative and how?

22. Challenge 5th Grade: MA.5.G.5.4 Derive and apply formulas for areas of parallelograms and trapezoids. What do you notice about the formulas? How do you prove it? What manipulative and how?

23. Virtual Manipulatives • National Library of Virtual Manipulatives • Gizmos- www.explorelearning.com

24. Journal Reflection Describe how we can use concrete resources to move students to the understanding of representational and abstract math concepts.